Adler Function, Sum Rules and Crewther Relation of Order O(alpha_s⁴): the Singlet Case

2012/06/30 by P. A. Baikov, K. G. Chetyrkin, J. H. Kühn +1
Physics and Astronomy · #hep-ph #hep-th

paper · pdf · doi:10.1016/j.physletb.2012.06.052

published as Phys.Lett. B714 (2012) 62-65 · 4 pages, 1 figure. Final published version

arxiv created 2012/10/10 · arxiv updated 2015/06/05

Abstract

The analytic result for the singlet part of the Adler function of the vector current in a general gauge theory is presented in five-loop approximation. Comparing this result with the corresponding singlet part of the Gross-Llewellyn Smith sum rule [1], we successfully demonstrate the validity of the generalized Crewther relation for the singlet part. This provides a non-trivial test of both our calculations and the generalized Crewther relation. Combining the result with the already available non-singlet part of the Adler function [2,3] we arrive at the complete \cal O(α_s⁴) expression for the Adler function and, as a direct consequence, at the complete \cal O(α_s⁴) correction to the e⁺ e^- annihilation into hadrons in a general gauge theory.

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